Question

An automobile accelerates from rest at $1+\sqrt{3}$ mph/sec for $9$ seconds. What is its velocity (in mph) after $9$ seconds?

• A. $12$
• B. $3+\sqrt{3}$
• C. $9+9\sqrt{3}$
• D. $9+\sqrt{3}$
• E. $9+3\sqrt{3}$

Answer 1

The correct option is C $9+9\sqrt{3}$

The initial velocity $v\left(0\right)=0$ is given and acceleration $a=1+\sqrt{3}mph/sec$

$\frac{dv\left(t\right)}{dt}=a\left(t\right)=1+\sqrt{3}$

$⟹v\left(t\right)=(1+\sqrt{3})t+C$

Now, at $t=0$, $v\left(0\right)=0+C⟹C=0$

$⟹v\left(t\right)=(1+\sqrt{3})t$

At, $t=9sec$

$v=9(1+\sqrt{3})=(9+9\sqrt{3})$ $mph$

Hence, answer is option-(C).